Semiempirical formula for multiple ionization cross sections of atoms by electron impact

Abstract

On the basis of experimental data on multiple-ionization cross sections σn of neutral atoms by electron impact a semiempirical formula for σn, n ⩾ 3, has been deduced where n is the number of ejected electrons. It has been shown that the cross section σn depends on three atomic parameters: the minimal ionization energy required to remove n electrons from the target, the total number of target electrons and the number of ejected electrons. The electron-impact energy dependence of the cross sections σn with different n is described by one universal function. As the number of ejected electrons n increases the cross section σn falls off approximately as σn ~ n−6.A comparison of σn calculated by the proposed semiempirical formula with available experimental data for the atomic targets from Ne to U and the number of the ejected electrons from n = 3 to n = 13 has been performed.For the first time, the formula suggested can be used for estimation of multiple-ionization cross sections σn, n ⩾ 3, from threshold up to high electron energies E ≈ 105 eV for an arbitrary atomic target.